A hand fan is made up of cloth fixed in between the metallic wires. It is in
the shape of a sector of a circle of radius 21 cm and of angle 120° as
shown in the figure. Calculate the area of the cloth used and also find the
total length of the metallic wire required to make such a fan.
Answers
Given:
A hand fan which is in the shape of a sector of a circle of radius 21 cm and of angle 120°, is made up of cloth fixed in between the metallic wires
To find:
(i) Area of the cloth used
(ii) The total length of the metallic wire required to make such a fan
Solution:
(i) Finding the area of the cloth used:
The radius of the sector of the circle, r = 21 cm
The measure of the central angle, θ = 120°
Here to get the area of the cloth used, we have to find the area of the sector.
So, we know the formula of the area of a sector when θ is given in terms of degrees is given as,
By substituting the given values in the formula, we get
Thus, the area of the cloth used is 462 cm².
(ii) Finding the total length of the metallic wire:
We will first find the arc length of the hand-made fan i.e.,
Now,
The required length of the metallic wire is given by,
= sum of all sides of the hand-made fan
= [2 × radius] + Arc length
substituting the value of radius and arc length
= [2 × 21] + 44
= 42 + 44
= 86 cm
Thus, the total length of the metallic wire required to make such a fan is 86 cm.
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